Multiply the following complex numbers: $({1+5i}) \cdot ({-4-4i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({1+5i}) \cdot ({-4-4i}) = $ $ ({1} \cdot {-4}) + ({1} \cdot {-4}i) + ({5}i \cdot {-4}) + ({5}i \cdot {-4}i) $ Then simplify the terms: $ (-4) + (-4i) + (-20i) + (-20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -4 + (-4 - 20)i - 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -4 + (-4 - 20)i - (-20) $ The result is simplified: $ (-4 + 20) + (-24i) = 16-24i $